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Dieter Ruoff - Solution of a non-Euclidean convexity problem
| DIETER RUOFF, Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S 0A2, Canada |
| Solution of a non-Euclidean convexity problem |
The curve that will be investigated is made up from the vertices of the
angles which have size 
, share the common chord
AB and lie
in one and the same halfplane with respect to the line through
AB.
It is a well-known fact that in Euclidean geometry these points form an
arc of a circle. Also, it is clear that any one of the given angles
can be moved into any other by a rotation. In non-Euclidean geometry
all this does not hold. A sketch of a convexity proof for this latter
setting will be provided.
